2.1 Current-Based State-Space Model of the DFIG

The DFIG voltage equations in the synchronous dq reference frame are given by:

where $v$, $i$, $\psi$, and $R$ denote voltage, current, flux linkage, and resistance, respectively. The subscripts $s$ and $r$ represent stator and rotor quantities, while $d$ and $q$ indicate the direct and quadrature axes. In addition, $\omega_{s}$ and $\omega_{r}$ are the synchronous and rotor electrical angular speeds, respectively.

The flux linkages are related to stator and rotor currents as follows:

where $X_{ss}$, $X_{rr}$, and $X_{m}$ denote the stator self-reactance, rotor self-reactance, and magnetizing reactance, respectively.

By substituting the flux-current relationships into the voltage equations and arranging the derivatives of the current variables, the current-based state-space model is obtained ^[11]. In this representation, input and output vectors are defined in the synchronous dq reference frame:

The system, control, output, and feedforward matrices are defined as:

where $s = (\bar{\omega}_{s} - \bar{\omega}_{r}) / \bar{\omega}_{s}$, $\alpha_{1} = \bar{X}_{ss} \bar{X}_{rr} - s \bar{X}_{m}^{2}$, $\alpha_{2} = \bar{X}_{m}^{2} - s \bar{X}_{ss} \bar{X}_{rr}$, $\beta_{s} = \bar{X}_{m} \bar{X}_{ss} (1 - s)$, $\beta_{r} = \bar{X}_{m} \bar{X}_{rr} (1 - s)$, $\sigma = 1 - \bar{X}_{m}^{2} / (\bar{X}_{rr} \bar{X}_{ss})$. Notice that $\alpha_{1}, \alpha_{2}, \beta_{s}$ and $\beta_{r}$ are expressed in terms of the slip s and the bar in the notation indicates per unit. In this formulation, matrix A describes the internal electrical dynamics of the DFIG, including resistive damping, magnetic coupling, and dq-axis cross-coupling. Matrix B maps the stator and rotor dq-axis voltage inputs to the current dynamics.

The model is completed by the rotor mechanical equation:

where in terms of state variables,

Fig. 2 shows the overall structure of the proposed DFIG model, including the mechanical system, state-space generator model, converter interface, and PVdq control. These components are interconnected to represent the dynamic behavior of the wind energy conversion system. Meanwhile, Tables 1 and 2 show the specifications of the wind turbine and DFIG model parameters, respectively.

Fig. 2. Overall structure of proposed DFIG model

2.2 DFIG Control Strategy

The rotor-side converter of a DFIG enables independent control of active and reactive power by regulating the rotor current components in the synchronous dq reference frame. To clarify this decoupling principle, Fig. 3 illustrates the relationship between rotor current components and stator active/reactive power under stator-flux orientation. In this reference frame, the q-axis rotor current $i_{rq}$ is mainly associated with electromagnetic torque and stator active power, whereas the d-axis rotor current $i_{rd}$ is mainly associated with stator reactive power or terminal voltage. Based on this principle, the PVdq control strategy is divided into two main paths: the P control loop for torque/active power regulation and the V control loop for voltage/reactive power regulation.

Fig. 3. DFIG power decoupling principle

After establishing the decoupling relationship, the torque reference used in the P control loop is derived from the maximum power extraction principle. The objective of a DFIG-based wind turbine is to extract the maximum available power from the wind. The aerodynamic power transferred from the wind to the turbine rotor is given by:

where $P_{av}$ is the available wind power, $\rho$ is the air density, $A$ is the swept area, $v_{w}$ is the wind speed, and $C_{p}$ is the power coefficient. The tip-speed ratio is defined as:

In below-rated operation, the pitch angle is kept constant and the turbine is controlled to operate near the optimal tip-speed ratio $\lambda_{opt}$, where $C_{p}$ reaches its maximum value. Under this condition, the optimal power can be expressed as:

where

Therefore, the corresponding torque set point for the MPPT-based speed control loop is given by:

This quadratic torque-speed relationship represents the MPPT characteristic in the below-rated region. In the rated and above-rated regions, the torque reference is limited by the rated power and coordinated with pitch control to avoid excessive power output.

Fig. 4. PVdq control strategy

The detailed PVdq control structure is shown in Fig. 4. Based on the decoupling principle in Fig. 3, the V control path generates the d-axis rotor current reference $i_{dr,ref}$ from the stator voltage error. The inner d-axis current controller then regulates $i_{dr}$ and produces the rotor voltage command $V_{dr}$ for terminal voltage and reactive power regulation. In the P control path, the MPPT lookup table uses $\omega_{r}$ to generate the torque set point $T_{SP}$, as derived in (22). This torque command is then converted into the q-axis rotor current reference $i_{qr,ref}$ according to the torque-current relationship under stator-flux orientation. The inner q-axis current controller regulates $i_{qr}$ to track $i_{qr,ref}$, thereby producing the electromagnetic torque required for MPPT operation and controlling the stator active power. For simulation and dynamic analysis, the proposed PVdq controller is represented in state-space form and implemented in MATLAB/Simulink via an S-function.

3.1 Validation and Error Metrics

The proposed virtual generator model for the DFIG-based wind turbine was implemented in MATLAB/Simulink and validated against measured SCADA data using three independent datasets. The SCADA data used in this study were recorded at 10-minute intervals for wind turbine supervisory monitoring from 2020 to 2024.

The accuracy was quantified using MAPE and %RMSE. MAPE measures the mean relative error and reduces sensitivity to absolute power scale, while %RMSE reflects the overall error magnitude and penalizes large deviations. These metrics are defined as follows:

3.2 Simulation Results Using Three SCADA Datasets

The simulation results are compared with three SCADA datasets and presented in Figs. 5–7. The datasets are selected to represent different operating conditions: dataset 1 corresponds to below-rated operation with gradual wind speed variation, dataset 2 includes operation near and above the rated wind speed where power limiting is expected, and dataset 3 represents below-rated operation with stronger wind speed fluctuations.

In dataset 2 (Fig. 6), when the wind speed reaches the rated region, the active power is maintained close to the rated value, which is consistent with the rated power regulation behavior. In datasets 1 and 3 (Figs. 5 and 7), the wind speed remains mostly below the rated region, so the active power varies with wind speed, and the model follows the SCADA trend and captures the main power changes over the evaluation interval. In addition to active-power validation, the grid voltage response is also compared with the SCADA voltage data. As shown in Figs. 5–7, the calculated voltage is regulated around the rated grid voltage of 690 V for all three datasets. The measured SCADA voltage also remains within approximately ±5% of the rated value, indicating that the voltage behavior is reasonably maintained under different wind conditions.

Fig. 5. Validation of Active Power and Grid Voltage for Dataset 1

Fig. 6. Validation of Active Power and Grid Voltage for Dataset 2

Fig. 7. Validation of Active Power and Grid Voltage for Dataset 3

Table 3 summarizes the active power validation errors obtained from the three SCADA datasets. The MAPE values are 6.17%, 6.87%, and 7.45% for datasets 1–3, respectively, while the corresponding %RMSE values are 5.97%, 6.10%, and 6.81%. The overall MAPE and %RMSE are 6.83% and 6.29%, respectively. Although dataset 3 shows the largest error due to stronger wind-speed fluctuations, the error variation among the three datasets remains relatively small, indicating that the proposed model provides consistent tracking performance under different operating conditions. Recent wind energy studies ^{[14], [15]} have reported similar error levels for model validation and power prediction, with MAPE values of approximately 6.9%–7.7%. Compared with these reported values, the overall MAPE of 6.83% obtained in this study indicates reasonably good accuracy for SCADA validation. Therefore, the proposed DFIG virtual generator model can reproduce the dominant active power behavior with acceptable accuracy while maintaining a compact structure suitable for digital twin applications.